Mathematics is not complete without a proof! The "Proof Wiki" offers up tens of thousands of proofs for all levels of mathematical interest. Another one of those web sites of incredible usefulness and value.
[20190312]
A compilation of useful links to various other blogs and web sites giving useful computational or analytical mathematical tools. This is intended to be of interest to the novice seeker of help in mastering some mathematics.
Showing posts with label Links to other sites. Show all posts
Showing posts with label Links to other sites. Show all posts
Tuesday, March 12, 2019
Wednesday, February 14, 2018
Simon's Course in Modern Analysis
Professor Barry Simon of Caltech has a series of books on modern analysis. As a prelude to this set he has written an ~130 page 'companion guide' which is available free from the Am. Math. Society at this link. It's a good read for anyone irrespective of level of math skills. Please avail yourself of this free publication! Give yourself a Valentine's Day present.
Now, right out of the gate, Prof. Simon tells us:
"Analysis is the infinitesimal calculus writ large. Calculus as taught to most high school students and college freshmen is the subject as it existed about 1750—I’ve no doubt that Euler could have gotten a perfect score on the Calculus BC advanced placement exam. Even “rigorous” calculus courses that talk about ε-δ proofs and the intermediate value theorem only bring the subject up to about 1890 after the impact of Cauchy and Weierstrass on real variable calculus was felt.
[20180214]
Now, right out of the gate, Prof. Simon tells us:
"Analysis is the infinitesimal calculus writ large. Calculus as taught to most high school students and college freshmen is the subject as it existed about 1750—I’ve no doubt that Euler could have gotten a perfect score on the Calculus BC advanced placement exam. Even “rigorous” calculus courses that talk about ε-δ proofs and the intermediate value theorem only bring the subject up to about 1890 after the impact of Cauchy and Weierstrass on real variable calculus was felt.
"This volume [vol 1] can be thought of as the infinitesimal calculus of the twentieth century. From that point of view, the key chapters are Chapter 4,
which covers measure theory—the consummate integral calculus—and the
first part of Chapter 6 on distribution theory—the ultimate differential calculus.
"But from another point of view, this volume is about the triumph of abstraction. Abstraction is such a central part of modern mathematics that one forgets that it wasn’t until Frechet’s 1906 thesis that sets of points with no a priori underlying structure (not assumed points in or functions on Rn) are considered and given a structure a posteriori (Frechet first defined abstract metric spaces). And after its success in analysis, abstraction took over significant parts of algebra, geometry, topology, and logic."
"But from another point of view, this volume is about the triumph of abstraction. Abstraction is such a central part of modern mathematics that one forgets that it wasn’t until Frechet’s 1906 thesis that sets of points with no a priori underlying structure (not assumed points in or functions on Rn) are considered and given a structure a posteriori (Frechet first defined abstract metric spaces). And after its success in analysis, abstraction took over significant parts of algebra, geometry, topology, and logic."
[20180214]
Mathematica and all that
At the risk of coming off as a shill for a commercial product (I'm not, I'm just an enthusiastic user) I would like to recommend the entire product line of mathematical tools available from Wolfram Research here. The flagship software is of course Mathematica. If you have not tried Mathematica you owe it to yourself, it's amazing and the number of avenues to access it has grown from Desktops to clouds and iOS availability. One never need be without sophisticated computational power! I urge you to visit their website!
[20140214]
[20140214]
Data collections
Sometimes one just needs to run some data through a calculation just to see if it works, no? Well, given enough complexity in the requirements, i.e. the data should have some fair amount of complexity, it is tedious to develop a database just for dry runs. Enter Wolfram! This software company which makes "Mathematica" and developed and maintains "Wolfram|Alpha" now offers collections of data just for those mathematicians needing to feed their latest creation. A link to the data collection is here.
[20180214]
[20180214]
Wednesday, January 3, 2018
Online source encyclopedia of math functions
Here's a handy and valuable online list of functions curated by NIST: DLMF.
Historical note. This is the online and updated version of the big, paperback reference book authored and edited by Abramowitz and Stegun. Additionally, the online version has been checked and validated by Professor Tom Apostol.
[20180103]
Historical note. This is the online and updated version of the big, paperback reference book authored and edited by Abramowitz and Stegun. Additionally, the online version has been checked and validated by Professor Tom Apostol.
[20180103]
Tuesday, January 2, 2018
John A. Wheeler's Papers
A well curated archive of Prof. Wheeler's publications is available at the "JAW Archive."
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[20120102]
Thursday, April 20, 2017
AMS open access notes
The AMS has opened a new repository of free access notes, papers and books. Access it here.
[170420]
[170420]
Friday, December 30, 2016
John Baez potpourri
Professor John Baez at UC Riverside has a web site with many unusual and interesting mathematically related demonstrations. Enjoy!
[161229]
[161229]
Sunday, June 19, 2016
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